Coulomb's Law

Coulomb’s law : Coulomb’s law states that the force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The direction of forces is along the line joining the two point charges.

Let q1 and q2 be two point charges placed in air or vacuum at a distance r apart (Fig.) 

              

Then, according to Coulomb’s law, 

F α q1 q2 / r^2

F= k q1 q2 / r^2

k is a constant of proportionality 

In air or vacuum, k = 1/4πεo, where εo is the permittivity of free space (i.e., vacuum) and the value of εo is 8.854 × 10^−12 C2 N^−1 m^−2.

F = q1 q2 / 4πεor^2      ...(1)

and 1/4πεo = 9 * 10^9 N m^2 C^-2

In the above equation, if q1 = q2 = 1C and  r = 1m then,

F = (9 * 10^9) x (1*1/1^2) = 9 * 10^9 N

One Coulomb is defined as the quantity of charge, which when placed at a distance of 1 metre in air or vacuum from an equal and similar charge, experiences a repulsive force of 9 × 10^9 N.

If the charges are situated in a medium of permittivity ε, then the magnitude of the force between them will be,

Fm = q1 q2 / 4πε r^2      ...(2)

Dividing equation (1) by (2)

F / Fm =  ε/εo = εr

The ratio  ε/εο = εr, is called the relative permittivity or dielectric constant of the medium. The value of εr for air or vacuum is 1.

∴  ε = εo εr

Since Fm =F/εr , the force between two point charges depends on the nature of the medium in which the two charges are situated.

Note :

A torsion balance is a sensitive device to measure force. It was also used later by Cavendish to measure the very feeble gravitational force between two objects, to verify Newton’s Law of Gravitation.